Parallel Magnetic Resonance Imaging (pMRI) reconstruction techniques, e.g. SENSE and Generalized Auto-calibrating Partially Parallel Acquisitions (GRAPPA), reduce scan time by under-sampling k-space, which directly improves temporal resolution in real-time cine imaging. GRAPPA, a k-space based pMRI technique, is widely used clinically for dynamic Magnetic Resonance (MR) imaging because of its robustness. GRAPPA reconstructs the missing k-space in each channel by applying convolution kernels on the acquired k-space. GRAPPA convolution kernels are estimated from fully-sampled k-space auto-calibration signal (ACS) lines using linear regression.
There are two widely-used methods to acquire ACS lines for GRAPPA reconstruction. The first method is to use a fully-sampled center of k-space block as the ACS lines in each frame; the second method is to use a separately acquired full-sampled k-space as the ASC lines. Each has limitations, for example, the first method lowers the efficiency and the second method is prone to motion artifacts.
In dynamic imaging, a variant of GRAPPA technique, the TGRAPPA method is commonly used. Multiple frame, uniformly down-sampled, temporally interleaved k-spaces are acquired, and the ACS lines are estimated using the temporal low-pass filtered images. In practice, an average-all-frame (AAF) method, i.e., the most extreme low-pass filtered image, is utilized as ACS lines of TGRAPPA.
Intuitively, ACS lines with a higher signal-to-noise ratio (SNR) should boost the accuracy of the kernel estimation and increase the SNR of GRAPPA reconstruction. Paradoxically, Sodickson et al. have found that higher SNR ACS lines used in GRAPPA may lead to lower SNR in the reconstructed images (Sodickson D K. Magn Reson Med 2000; 44(2):243-251; Yeh E N, et. al. Magn Reson Med 2005; 53(6):1383-1392). The reason is that the higher SNR in the ACS lines causes higher condition number of the GRAPPA kernel encoding equation. If the condition number is too high, the GRAPPA kernel encoding equations become ill-conditioned, and then the estimated GRAPPA kernel is corrupted by high random noise. Therefore, the corresponding GRAPPA reconstruction has lower SNR.